Bitcoin Halving Process Visualization

How Bitcoin’s supply approaches 21 million through programmatic halving

Overview

Bitcoin’s 21 million coin cap is maintained through an elegant mathematical design that combines block rewards and halving. This visualization shows how the supply approaches its maximum through programmatic halving every 210,000 blocks (approximately 4 years).

Cumulative Bitcoin Supply Over Time

Note

Bitcoin’s block reward system creates new bitcoins approximately every 10 minutes, starting at 50 BTC per block in 2009. Every 210,000 blocks (roughly 4 years), this reward cuts in half—from 50 to 25, then 12.5, 6.25, 3.125, and so on—creating a predictable supply schedule. This halving process forms a geometric series that mathematically converges to approximately 21 million BTC, with the supply curve asymptotically approaching but never quite reaching the cap. By around 2140, when the block reward becomes smaller than Bitcoin’s smallest unit (1 satoshi), no new bitcoins will be created, and miners will rely entirely on transaction fees for compensation.

A satoshi is the smallest unit of Bitcoin, named after its pseudonymous creator Satoshi Nakamoto. One satoshi equals 0.00000001 BTC, meaning there are exactly 100 million satoshis in a single bitcoin. This tiny denomination allows for microtransactions and ensures Bitcoin remains divisible and practical even if its value increases dramatically, similar to how a dollar can be divided into 100 cents.

Remaining Bitcoin to be Mined

Y-axis log scale reveals the consistent exponential decay - the remaining supply halves with each halving event.

Block Reward Decay Over Halving

Note

Bitcoin miners receive a fixed number of newly created bitcoins (the “block reward”) for successfully mining each block, which occurs approximately every 10 minutes. This reward started at 50 BTC in 2009 and automatically halves every 210,000 blocks (roughly every 4 years), currently sitting at 3.125 BTC as of 2024. Through this systematic halving process, the total supply of Bitcoin will asymptotically approach but never exceed 21 million coins, with the final bitcoin expected to be mined around the year 2140. Y-axis log scale again reveals the consistent exponential decay.

Bitcoin Halving Schedule

Halving #	Year	Block Reward	BTC Mined	Cumulative Supply	% of Cap
0	~2009	50.00000000	10,500,000.000	10,500,000.000	50.000000000%
1	~2013	25.00000000	5,250,000.000	15,750,000.000	75.000000000%
2	~2017	12.50000000	2,625,000.000	18,375,000.000	87.500000000%
3	~2021	6.25000000	1,312,500.000	19,687,500.000	93.750000000%
4	~2025	3.12500000	656,250.000	20,343,750.000	96.875000000%
5	~2029	1.56250000	328,125.000	20,671,875.000	98.437500000%
6	~2033	0.78125000	164,062.500	20,835,937.500	99.218750000%
7	~2037	0.39062500	82,031.250	20,917,968.750	99.609375000%
8	~2041	0.19531250	41,015.625	20,958,984.375	99.804687500%
9	~2045	0.09765625	20,507.812	20,979,492.188	99.902343750%
10	~2049	0.04882812	10,253.906	20,989,746.094	99.951171875%
11	~2053	0.02441406	5,126.953	20,994,873.047	99.975585938%
12	~2057	0.01220703	2,563.477	20,997,436.523	99.987792969%
13	~2061	0.00610352	1,281.738	20,998,718.262	99.993896484%
14	~2065	0.00305176	640.869	20,999,359.131	99.996948242%
15	~2069	0.00152588	320.435	20,999,679.565	99.998474121%
16	~2073	0.00076294	160.217	20,999,839.783	99.999237061%
17	~2077	0.00038147	80.109	20,999,919.891	99.999618530%
18	~2081	0.00019073	40.054	20,999,959.946	99.999809265%
19	~2085	0.00009537	20.027	20,999,979.973	99.999904633%
20	~2089	0.00004768	10.014	20,999,989.986	99.999952316%
21	~2093	0.00002384	5.007	20,999,994.993	99.999976158%
22	~2097	0.00001192	2.503	20,999,997.497	99.999988079%
23	~2101	0.00000596	1.252	20,999,998.748	99.999994040%
24	~2105	0.00000298	0.626	20,999,999.374	99.999997020%
25	~2109	0.00000149	0.313	20,999,999.687	99.999998510%
26	~2113	0.00000075	0.156	20,999,999.844	99.999999255%
27	~2117	0.00000037	0.078	20,999,999.922	99.999999627%
28	~2121	0.00000019	0.039	20,999,999.961	99.999999814%
29	~2125	0.00000009	0.020	20,999,999.980	99.999999907%
30	~2129	0.00000005	0.010	20,999,999.990	99.999999953%
31	~2133	0.00000002	0.005	20,999,999.995	99.999999977%
32	~2137	0.00000001	0.002	20,999,999.998	99.999999988%

Note

Current halving (2024-2028) is halving #4
By halving #10 (around 2049), 99.9% of all Bitcoin will be mined
By 2101 (Halving #23), only 1.25 Bitcoin will be available for mining
Final Bitcoin will be mined around year 2140

Summary Statistics

Metric	Value
First Block Reward	50 BTC
Current Block Reward	3.125 BTC (as of 2024)
Total Halvings Until ~0	33
Years to Mine All Bitcoin	~128.0 years
Bitcoin Mined in First 4 Years	10,500,000 BTC (50% of total)
Bitcoin After 10 Halvings	20,979,492 BTC (99.80% of cap)
Estimated Final Supply	20,999,999.9769 BTC

The Mathematics

The total supply follows a geometric series:

\[ \text{Total Supply} = \sum_{n=0}^{64} 210{,}000 \times \frac{50}{2^n} \] —

Session Information

Click to view session information

-----
numpy               2.3.4
pandas              2.3.3
plotly              6.4.0
session_info        v1.0.1
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Click to view modules imported as dependencies

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IPython             9.7.0
jupyter_client      8.6.3
jupyter_core        5.9.1
jupyterlab          4.4.10
notebook            7.4.7
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Python 3.14.0 (v3.14.0:ebf955df7a8, Oct  7 2025, 08:20:14) [Clang 16.0.0 (clang-1600.0.26.6)]
macOS-15.3.1-arm64-arm-64bit-Mach-O
-----
Session information updated at 2026-01-16 13:34

--- title: "Bitcoin Halving Process Visualization" subtitle: "How Bitcoin's supply approaches 21 million through programmatic halving" format: html: theme: sandstone code-fold: true code-tools: true code-summary: "Show code" embed-resources: true embed-math: true toc: true toc-depth: 2 execute: echo: false warning: false --- ```{python} #| label: setup import session_info import pandas as pd import numpy as np import plotly.graph_objects as go import plotly.express as px from plotly.subplots import make_subplots ``` ```{python} #| label: data-generation # Generate Bitcoin halving data def generate_halving_data(): data = [] block_reward = 50 cumulative_supply = 0 blocks_per_halving = 210000 # Generate data for approximately 34 halvings for halving in range(34): year = 2009 + (halving * 4) blocks_in_period = blocks_per_halving btc_in_period = blocks_in_period * block_reward cumulative_supply += btc_in_period data.append({ 'halving': halving, 'year': year, 'block_reward': block_reward, 'cumulative_supply': cumulative_supply, 'btc_per_period': btc_in_period, 'percent_of_cap': (cumulative_supply / 21000000) * 100, 'remaining_supply': 21000000 - cumulative_supply }) block_reward = block_reward / 2 # Stop when block reward becomes negligible if block_reward < 0.00000001: break return pd.DataFrame(data) df = generate_halving_data() ``` ### Overview Bitcoin's 21 million coin cap is maintained through an elegant mathematical design that combines block rewards and halving. This visualization shows how the supply approaches its maximum through programmatic halving every 210,000 blocks (approximately 4 years). ### Cumulative Bitcoin Supply Over Time ```{python} #| label: cumulative-supply-chart fig1 = go.Figure() # Add cumulative supply line fig1.add_trace(go.Scatter( x=df['year'], y=df['cumulative_supply'], mode='lines+markers', name='Total BTC Supply', line=dict(color='#F97316', width=3), marker=dict(size=6, color='#F97316'), hovertemplate='Year: %{x} ' + 'Supply: %{y:,.0f} BTC ' + '<extra></extra>' )) # Add 21M cap line fig1.add_trace(go.Scatter( x=df['year'], y=[21000000] * len(df), mode='lines', name='21M Cap', line=dict(color='#EF4444', width=2, dash='dash'), hovertemplate='21M Cap<extra></extra>' )) fig1.update_layout( template='plotly_dark', plot_bgcolor='#1F2937', paper_bgcolor='#111827', height=500, xaxis=dict( title='', showgrid=True, gridcolor='#374151', tickfont=dict(size=12) ), yaxis=dict( title='BTC Supply (millions)', showgrid=True, gridcolor='#374151', tickformat='.1f', ticksuffix='M', tickvals=[0, 5000000, 10000000, 15000000, 20000000, 21000000], ticktext=['0M', '5M', '10M', '15M', '20M', '21M'], tickfont=dict(size=11) ), legend=dict( orientation='h', yanchor='bottom', y=1.02, xanchor='right', x=1 ), hovermode='x unified' ) fig1.show() ``` ::: {.callout-note} Bitcoin's block reward system creates new bitcoins approximately every 10 minutes, starting at 50 BTC per block in 2009. Every 210,000 blocks (roughly 4 years), this reward cuts in half—from 50 to 25, then 12.5, 6.25, 3.125, and so on—creating a predictable supply schedule. This halving process forms a geometric series that mathematically converges to approximately 21 million BTC, with the supply curve asymptotically approaching but never quite reaching the cap. By around 2140, when the block reward becomes smaller than Bitcoin's smallest unit (1 satoshi), no new bitcoins will be created, and miners will rely entirely on transaction fees for compensation. A satoshi is the smallest unit of Bitcoin, named after its pseudonymous creator Satoshi Nakamoto. One satoshi equals 0.00000001 BTC, meaning there are exactly 100 million satoshis in a single bitcoin. This tiny denomination allows for microtransactions and ensures Bitcoin remains divisible and practical even if its value increases dramatically, similar to how a dollar can be divided into 100 cents. ::: ### Remaining Bitcoin to be Mined ```{python} #| label: remaining-supply-chart fig2 = go.Figure() # Add remaining supply line fig2.add_trace(go.Scatter( x=df['year'], y=df['remaining_supply'], mode='lines+markers', name='BTC Remaining', line=dict(color='#3B82F6', width=3), marker=dict(size=6, color='#3B82F6'), hovertemplate='Year: %{x} ' + 'Remaining: %{y:,.0f} BTC ' + '% Remaining: %{customdata:.2f}% ' + '<extra></extra>', customdata=(df['remaining_supply'] / 21000000) * 100 )) fig2.update_layout( template='plotly_dark', plot_bgcolor='#1F2937', paper_bgcolor='#111827', height=500, xaxis=dict( title='', showgrid=True, gridcolor='#374151', tickfont=dict(size=11) ), yaxis=dict( title='', type='log', showgrid=True, gridcolor='#374151', tickformat=',', tickfont=dict(size=11) ), legend=dict( orientation='h', yanchor='bottom', y=1.02, xanchor='right', x=1 ), hovermode='x unified' ) fig2.show() ``` Y-axis log scale reveals the consistent exponential decay - the remaining supply halves with each halving event. ### Block Reward Decay Over Halving ```{python} #| label: block-reward-chart # Show only first 16 halvings for better visualization df_subset = df.head(33) fig3 = go.Figure() fig3.add_trace(go.Bar( x=df_subset['halving'], y=df_subset['block_reward'], name='Block Reward', marker_color='#F97316', hovertemplate='Halving #: %{x} ' + 'Year: ~%{customdata} ' + 'Block Reward: %{y:.8f} BTC ' + '<extra></extra>', customdata=df_subset['year'] )) fig3.update_layout( template='plotly_dark', plot_bgcolor='#1F2937', paper_bgcolor='#111827', height=500, xaxis=dict( title='Halving Number', showgrid=True, gridcolor='#374151', tickfont=dict(size=11), tickmode='linear', tick0=0, dtick=1 ), yaxis=dict( title='Block Reward (BTC)', type='log', showgrid=True, gridcolor='#374151', tickfont=dict(size=11) ), hovermode='x unified' ) fig3.show() ``` ::: {.callout-note} Bitcoin miners receive a fixed number of newly created bitcoins (the "block reward") for successfully mining each block, which occurs approximately every 10 minutes. This reward started at 50 BTC in 2009 and automatically halves every 210,000 blocks (roughly every 4 years), currently sitting at 3.125 BTC as of 2024. Through this systematic halving process, the total supply of Bitcoin will asymptotically approach but never exceed 21 million coins, with the final bitcoin expected to be mined around the year 2140. Y-axis log scale again reveals the consistent exponential decay. ::: ### Bitcoin Halving Schedule {.tabset} ```{python} #| label: data-table # Show first 33 halvings in a formatted table df_display = df.head(33).copy() df_display['year'] = '~' + df_display['year'].astype(str) df_display['block_reward'] = df_display['block_reward'].apply(lambda x: f'{x:.8f}') df_display['btc_per_period'] = df_display['btc_per_period'].apply(lambda x: f'{x:,.3f}') df_display['cumulative_supply'] = df_display['cumulative_supply'].apply(lambda x: f'{x:,.3f}') df_display['percent_of_cap'] = df_display['percent_of_cap'].apply(lambda x: f'{x:.9f}%') df_display = df_display[['halving', 'year', 'block_reward', 'btc_per_period', 'cumulative_supply', 'percent_of_cap']] df_display.columns = ['Halving #', 'Year', 'Block Reward', 'BTC Mined', 'Cumulative Supply', '% of Cap'] # Style the current halving (2024-2028) styled_df = df_display.style.set_properties(**{ 'background-color': '#1F2937', 'color': '#D1D5DB', 'border-color': '#374151' }).set_table_styles([ {'selector': 'th', 'props': [('background-color', '#F97316'), ('color', 'white'), ('font-weight', 'bold')]}, {'selector': 'tr:nth-of-type(5)', 'props': [('background-color', '#7C2D12')]} # Highlight current halving ]).hide(axis='index') styled_df ``` ::: {.callout-note} - Current halving (2024-2028) is halving #4 - By halving #10 (around 2049), 99.9% of all Bitcoin will be mined - By 2101 (Halving #23), only 1.25 Bitcoin will be available for mining - Final Bitcoin will be mined around year 2140 ::: ### Summary Statistics ```{python} #| label: summary-stats from IPython.display import Markdown stats = f""" | Metric | Value | |--------|-------| | **First Block Reward** | 50 BTC | | **Current Block Reward** | 3.125 BTC (as of 2024) | | **Total Halvings Until ~0** | {len(df)} | | **Years to Mine All Bitcoin** | ~{df.iloc[-1]['year'] - 2009} years | | **Bitcoin Mined in First 4 Years** | {df.iloc[0]['cumulative_supply']:,.0f} BTC (50% of total) | | **Bitcoin After 10 Halvings** | {df.iloc[9]['cumulative_supply']:,.0f} BTC ({df.iloc[8]['percent_of_cap']:.2f}% of cap) | | **Estimated Final Supply** | 20,999,999.9769 BTC | """ Markdown(stats) ``` ### The Mathematics The total supply follows a geometric series: $$ \text{Total Supply} = \sum_{n=0}^{64} 210{,}000 \times \frac{50}{2^n} $$ --- ### Session Information <div style="font-size: 0.8em;"> ```{python} session_info.show() ``` </div>